Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`g(x) = x/2 + 2/x, x > 0`

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`g(x) = 1/(x^2 + 2)`

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

`f(x) = xsqrt(1-x), x > 0`

Prove that the following function do not have maxima or minima:

f(x) = e^x

Prove that the following function do not have maxima or minima:

g(x) = logx

Prove that the following function do not have maxima or minima:

h(x) = x³ + x² + x + 1

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

`f(x) =x^3, x in [-2,2]`

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

f (x) = sin x + cos x , x ∈ [0, π]

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

`f(x) = 4x - 1/x x^2, x in [-2 ,9/2]`

Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

f (x) = (x −1)² + 3, x ∈[−3, 1]

Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x².

Find both the maximum value and the minimum value of 3x⁴ − 8x³ + 12x² − 48x + 25 on the interval [0, 3].

Find the maximum value of 2x³ − 24x + 107 in the interval [1, 3]. Find the maximum value of the same function in [−3, −1].

It is given that at x = 1, the function x⁴− 62x² + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.

Find the maximum and minimum values of x + sin 2x on [0, 2π].

Find two positive numbers x and y such that their sum is 35 and the product x²y⁵ is a maximum.